Unweighted Index Numbers

There are two methods of constructing unweighted index numbers. (1) Simple Aggregative Method (2) Simple Average of Relative Method

Simple Aggregative Method:

In this method, the total of the prices of commodities in a given (current) years is divided by the total of the prices of commodities in a base year and expressed as percentage.

{P_{on}} = \frac{{\sum {P_n}}}{{\sum {P_o}}} \times 100

Simple Average of Relatives Method:

In this method, we compute price relative or link relatives of the given commodities and then use one of the averages such as arithmetic mean, geometric mean, median etc. If we use arithmetic mean as average, then

{P_{on}} = \frac{1}{n}\sum \left( {\frac{{{P_n}}}{{{P_o}}}} \right) \times 100


The simple average of relative method is very simple and easy to apply is superior to simple aggregative method. This method has only disadvantage that it gives equal weight to all items.

Example:

The following are the prices of four different commodities for 1990 and1991. Compute a price index by (1) Simple aggregative method and (2) Average of price relative method by using both arithmetic mean and geometric mean, taking1990 as base.

Commodity
Cotton
Wheat
Rice
Gram
Price in1990
909
288
767
659
Price in 1991
874
305
910
573

Solution:
The necessary calculations are given below:

Commodity
Price in1990
{P_o}
Price in 1991
{P_n}
Price Relative
P = \frac{{{P_n}}}{{{P_o}}} \times 100
\log P
Cotton
909
874
\frac{{874}}{{909}} \times 100 = 69.15
1.9829
Wheat
288
305
\frac{{305}}{{288}} \times 100 = 105.90
2.0249
Rice
767
910
\frac{{910}}{{767}} \times 100 = 118.64
2.0742
Gram
659
573
\frac{{573}}{{659}} \times 100 = 86.95
1.9393
Total
\sum {P_o} = 2623
\sum {P_n} = 2662
\sum P = 407.64
\begin{gathered} \sum \log P \\ = 8.0213\\ \end{gathered}

(1) Simple Aggregative Method:

{P_{on}} = \frac{{\sum {P_n}}}{{\sum {P_o}}} \times 100 = \frac{{2662}}{{2623}} \times 100 = 101.49

(2) Average of Price Relative Method (using arithmetic mean):

{P_{on}} = \frac{1}{n}\sum \left( {\frac{{{P_n}}}{{{P_o}}}} \right) \times 100 = \frac{1}{4}\left( {407.64} \right) = 101.91

Average of Price Relative Method (using geometric mean)

{P_{on}} = anti\log \left( {\frac{{\sum \log P}}{n}} \right) = anti\log \left( {\frac{{8.0213}}{4}} \right) = 101.23